Tensor-decomposition-based inverse characterization of flow stress for very-high strain-rate impact

Accurate characterization of flow stress under very-high strain-rate loading remains challenging owing to the limited accessibility of direct experimental measurements and the large uncertainties associated with conventional extrapolation approaches. This study proposes a Tensor-Decomposition-Based Extrapolation and Dynamic Identification of Flow Stress (TEDI-FS) framework for inverse characterization of flow stress under very-high strain-rate conditions. Within the proposed framework, flow stress is represented by a non-negative rank-2 canonical polyadic (CP) decomposition, enabling structured separation of strain, strain-rate and temperature effects while preserving non-negativity and physical interpretability. Material parameters are first identified within an experimentally accessible domain spanning from quasi-static to split Hopkinson pressure bar (SHPB) strain-rates, avoiding predefined coupling assumptions embedded in conventional flow-stress equations. To extend the flow-stress representation beyond the SHPB-accessible strain-rates, the strain-rate-dependent latent modes are extrapolated under consistency constraints and subsequently identified through coupled Taylor-Hopkinson impact experiments and explicit finite-element simulations. The proposed rank-2 framework demonstrates improved extrapolation robustness and predictive accuracy, achieving good agreement with Taylor-Hopkinson impact responses up to strain-rates of approximately 10⁵ s⁻¹ and outperforming conventional and rank-1 extrapolation-based flow-stress models. The proposed TEDI-FS framework establishes a physically interpretable, mathematically consistent and experimentally constrained methodology for extending flow-stress characterization towards very-high strain-rate regimes.